Reference Crust-Mantle Density Contrast Beneath Antarctica Based on the Vening Meinesz-Moritz Isostatic Inverse Problem and CRUST2.0 Seismic Model

EARTH SCIENCES RESEARCH JOURNAL

Earth Sci. Res. SJ. Vol. 17, No. 1 (June, 2013): 7 -12

GEOPHYSICS Reference crust-mantle density contrast beneath Antarctica based on the Vening Meinesz-Moritz isostatic inverse problem and CRUST2.0 seismic model

Robert Tenzer1 and Mohammad Bagherbandi2,3

1 Institute of Geodesy and Geophysics, School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan, China 2 Division of Geodesy and Geoinformatics, Royal Institute of Technology (KTH), SE-10044 Stockholm, Sweden 3 Department of Industrial Development, IT and Land Management University of Gävle, SE-80176 Gävle, Sweden

ABSTRACT Key words: Antarctica, crust, gravity, isostasy, mantle, Moho interface. The crust-mantle (Moho) density contrast beneath Antarctica was estimated based on solving the Vening Meinesz-Moritz isostatic problem and using constraining information from a seismic global crustal model (CRUST2.0). The solution was found by applying a least-squares adjustment by elements method. Global geopotential model (GOCO02S), global topographic/bathymetric model (DTM2006.0), ice-thickness data for Antarctica (assembled by the BEDMAP project) and global crustal model (CRUST2.0) were used for computing isostatic gravity anomalies. Since CRUST2.0 data for crustal structures under Antarctica are not accurate (due to a lack of seismic data in this part of the world), Moho density contrast was determined relative to a reference homogenous crustal model having 2,670 kg/m3 constant density. Estimated values of Moho density contrast were between 160 and 682 kg/m3. The spatial distribution of Moho density contrast resembled major features of the Antarctic’s continental and surrounding oceanic tectonic plate configuration; maxima exceeding 500 kg/m3 were found throughout the central part of East Antarctica, with an extension beneath the Transantarctic mountain range. Moho density contrast in West Antarctica decreased to 400-500 kg/m3, except for local maxima up to ~ 550 kg/m3 in the central Antarctic Peninsula.

RESUMEN Palabras clave: Antártida, corteza terrestre, manto terrestre, gravedad, isostasia, Discontinuidad de Mohorovičić El contraste de densidad de la discontinuidad de Mohorovičić (Moho) debajo de la Antártida fue estimado con base en la solución del problema isostático Vening Meinesz-Moritz y a partir de datos obtenidos con el modelo sísmico de la corteza global (CRUST2.0). La solución se encontró a través de un ajuste al método de mínimos cuadrados por el método de elementos. El modelo geopotencial global (GOCO02S), el modelo topográfico/ batimétrico (DTM2006.0), los datos de espesor del hielo para la Antártida (reunidos por el proyecto BEDMAP) y el modelo sísmico de corteza global (CRUST2.0) fueron utilizados para calcular las anomalías gravitatorias isostáticas. Ya que los datos de CRUST2.0 para las estructuras de la corteza en la Antártida no son exactos (debido a la falta de información sísmica para esta parte del planeta), el contraste de densidad de la Discontinuidad de Mohorovičić fue determinado a partir de un modelo de corteza homogéneo que tiene una densidad constante de 2,670 kg/m3. Los valores estimados del contraste de densidad de la Moho se encontraron entre 160 y 682kg/ m3. La distribución espacial del contraste de densidad de la Moho exhibe mayores rasgos en la configuración de la plancha tectónica de la Antártida continental y su alrededor oceánico. El valor máximo encontrado excede los Record 500 kg/m3 y se ubica en la parte Este continental, con extensión en las Montañas Transantárticas. El contraste de densidad de la Moho (zona de transición entre la corteza y el manto terrestre) en el Oeste de la Antártida osciló Manuscript received: 23/10/2012 entre 400-500 kg/m3, excepto para la máxima local de ~ 550 kg/m3, en el centro de la Península Antártida. Accepted for publication: 04/04/2013

Introduction based on localised controlled source seismic experiments. Passive seismic studies, based on earthquakes occurring mostly outside the Antarctic tec- Current knowledge about the lithospheric structure beneath An- tonic plate (due to a lack of intra-plate seismicity within the Antarctic tarctica is limited due to a low spatial coverage of high-quality seismic plate (Okal, 1981), still represent the primary source of information. data. Seismic studies by Kogan (1972) and Ito and Ikami (1986) were Studies based on an analysis of surface wave velocity can be found in Robert Tenzer and Mohammad Bagherbandi

Evison et al., (1960), Kovach and Press (1961), Bentley and Ostenso the Bouguer gravity reduction term , which was defined by the (1962), Dewart and Toksoz (1965), Adams (1971), Knopoff and Vane coefficients of global topographic/bathymetric (density) spherical functions (1978), Rouland et al., (1985), Forsyth et al., (1987), Roult et al., (1994) . The coefficients were defined as (Sjöberg, 2009): and Bannister et al., (2003). Seismic receiver function analysis has been carried out by Reading (2006), Lawrence et al., (2006) and Winberry , (4) and Anandakrishnan (2004). Ritzwoller et al., (2001) used the simultaneous inversion of broadband group velocity measurements to compile a seismic model of the crust and upper mantle beneath Antarctica and surrounding oceans. Some studies have been based on airborne gravi- where is the (fully-normalised) surface spherical harmonic function ty surveys, for instance by Studinger et al., (2004, 2006). Llubes et al., of degree n and order m . The density distribution function equals (2003) used CHAMP satellite gravity data for estimating crust thickness on land and ocean density contrast is defined as: ; where c is in Antarctica. More recently, Block et al., (2009) have estimated crust wareference crust density and mean saltwater density. Ice and sediment thickness in Antarctica using GRACE gravity data. density contrasts were defined relative to reference crust density c. Nominal ~ c Despite some authors having investigated Antarctic crust thickness, (zero-degree) compensation attraction g0 stipulated at the sphere of radius R studies addressing lithosphere density structure and density interface in was computed as from (Sjöberg, 2009): this part of the world are rare. This study was thus aimed at investigating Moho density contrast beneath Antarctic continental and surrounding oceanic crustal structures. Since large areas of Antarctica are not yet suffi- ciently covered by seismic surveys, current knowledge about crust density structure is not complete and accurate. A simple model of 2,670 kg/m3 , (5) homogenous crust reference density was thus adopted and Moho density contrast was estimated regarding such crustal density. This involved where , and T0 and are the adopted nominal mean values applying the method recently developed by Sjöberg (2009) and Sjöberg of Moho depth and density contrast, respectively. and Bagherbandi (2011). Estimation principle Isostatic model Least-squares analysis was used for estimating T and ∆ρ . The lineari- The generic expression of solving the Vening Meinesz-Moritz isostatic pro- sed observation equation involved expanding the integral term on the left- blem was formulated in the following form (Sjöberg and Bagherbandi, 2011): hand side of equation (1) into a Taylor series. The subsequent substitution of the first two terms in the series for s n+3 from equation (3) to equation −GR∫∫ ∆ρ( Ω′′) K( ψ ,sd) Ω = ∆ g i ( r, Ω), (1) (1) yielded (Sjöberg and Bagherbandi, 2011): Φ

where G = 6.674×10-11 m3 kg-1 s-2 is Newton’s gravitational constant, R = 6371×103 m Earth’s mean radius, ∆ρ Moho density contrast, ∆g i (approximate) isostatic gravity anomaly (cf. Sjöberg, 2009), K the integral . (6) kernel function, and dΩ′ = cosφ′dφ′dλ′ the infinitesimal surface element on the unit sphere. The 3-D position was defined in the spherical coordi- nates system (r,Ω), where r is the spherical radius and Ω = (φ,λ) denotes From equation (5), the linearised observation equation for product the spherical direction with spherical latitude φ and longitude λ . The full T ∆ρ was found in the following form: spatial angle is denoted as . Integral kernel K in equation (1) was defined for parametersψ and . (7) s, where ψ is the spherical distance between observation and (running) integration points (r,Ω) and (r′,Ω′), and s a ratio function of the Moho depth T and Earth’s mean radius R, i.e. s = 1−τ = 1−T / R. The spectral Approximation of term in equation (7) by yiel- representation of K was given by (Sjöberg, 2009): ded the linearised observation equation for ∆ρ in the following form: ∞ n +1 n+3 , (2) K(ψ , s) = ∑ (1− s ) Pn (cosψ ) . (8) n=0 n + 3

where Pn is the Legendre polynomial of degree n for the argument of Least-squares analysis combined the estimated product of T and ∆ρ cosine of the spherical distance ψ . with a priori values t and κ of such parameters for obtaining improved i The isostatic gravity anomaly ∆g computed at position (r,Ω) was estimates of T and ∆ρ. The system of observation equations was given in defined as follows (cf. Vening Meinesz, 1931): the following vector-matrix form:

∆g i (r,Ω) = ∆g B (r,Ω)+ g c (r,Ω) = 0, (3) , (9)

where ∆g B is the refined Bouguer gravity anomaly, and g c the gravi- where is the vector of residuals. Parameter vector x and observation tational attraction of isostatic compensation masses (see also Bjerhammar, vector l read: 1962, Chap. 14, eqn. 5; Moritz, 1990). The spectral representation of isostatic gravity anomaly ∆g i was defined in terms of spherical harmonics , of degree n and order m. The numerical coefficients were generated (10) from spherical harmonic coefficients of gravity anomaly after applying Reference crust-mantle density contrast beneath Antarctica based on the Vening Meinesz-Moritz isostatic inverse problem and CRUST2.0 seismic model

2 Elements l1 , l2 and l3 of the observation vector l were formed, respecti- where unit weight variance σ 0 reads was: vely, by observables T ∆ρ, ∆ρ and T. Parameter vector x was defined for 2 T −1 unknown corrections and dκ to a priori (initial) values of T and ∆ρ. σ 0 = l Q (l − A xˆ ). (13) The solution of normal equations was found by solving: Data acquisition , (11) The computation of isostatic gravity anomalies over the study area

Covariance matrix Q xˆ of the estimated parameters was computed of Antarctica required the application of gravity corrections due to from: rough topography, continental ice sheet and variable geological structu- 2 −1 Q xˆ = σ 0 N , (12) re (mainly large sediment deposits). The three largest mountain ranges on the Antarctic continent are the Transantarctic Mountains, the West and East Antarctica ranges. The Transantarctic Mountains is formed by a mountain range extending, with some interruptions, across the continent from Cape Adare in northern Victoria Land to Coats Land. These mountains serve as the natural geographical division between East and West Antarctica. Absolute maxima of topographic gravity correction in this part of the world reach ~400 mGal (Tenzer et al., 2009). Approxi- mately 98% of the land in Antarctica is covered by the continental ice sheet, thickness exceeding 2 km, while only about 0.32% of the land is ice-free. Maximum ice thickness is 4,776 m. The ice mass thus represents a significant contribution to the gravity field. Another significant gravity field contribution along the continental shelf of Antarctica is due to the presence of large sedimentary basins. Additional large sedimentary deposits exist inland of Antarctica (see Studinger et al., 2003; Bamber et al., 2006). Tenzer et al., (2010, 2012) have demonstrated that ice and sediment stripping corrections to gravity data in Antarctica reach about 300 mGal and 60 mGal, respectively. The global geopotential model (GOCO02S), the global topographic/ bathymetric model (DTM2006.0), ice-thickness data for Antarctica (assembled by the BEDMAP project; Lythe et al., 2001) and sediment density and thickness data from the global crustal model (CRUST2.0) were used in this study to compute isostatic gravity anomalies over the study area of Antarctica bounded by parallel 60 arc-deg of southern geographical latitude. All gravity computations were realized on a 2×2 arc-deg surface grid. Coefficients from the combined GRACE and GOCE satellite global Fig. 1 The Earth’s solid topography generated on a 2×2 arc-deg grid using geopotential model GOCO02S (Goiginger et al., 2011) with a spectral DTM2006.0 coefficients complete to degree/order of 180. Values are in km. resolution complete to degree 180 spherical harmonics were used for pro- ducing gravity anomalies. Refined Bouguer gravity anomalies were ob-

Fig. 2 Refined Bouguer gravity anomalies computed on a 2×2 arc-deg surface grid with a spectral resolution complete to degree 180 of spherical harmonics. Values Fig. 3 Crust-mantle density contrast computed on a 2×2 arc-deg grid using a are in miligals. combined least-squares method. Values are in kg/m3. Robert Tenzer and Mohammad Bagherbandi tained after applying Bouguer gravity reductions to GOCO02S gravity CRUST2.0 The variance-covariance matrix Q in the least-squares es- anomalies. The spherical Bouguer gravity reduction was computed using timation model (in eqn. 11) was computed from (cf. Sjöberg and coefficients from the global topographic/bathymetric model DTM2006.0 Bagherabndi, 2011): (Pavlis et al., 2007) complete to spherical harmonic degree 180. The ave-  σ 2 σ 2 / t 0  3  1 1  rage density of upper continental crust 2,670 kg/m (Hinze, 2003) was 2 2 3 Q = σ 1 / t σ 2 0  , (14) adopted as reference crust density. The ocean density contrast 1,643 kg/m  2  0 0 σ corresponds to mean seawater density 1,027 kg/m3, Updated 5×5 arc-min  3  ice-thickness data for Antarctica assembled by the BEDMAP project were used to compute the ice (density contrast) stripping gravity correction. where σ 1 and σ 3 are the standard errors of T ∆ρ and T, respectively, 2 2 2 2 2 4 The ice stripping gravity correction was computed with a spectral reso- and σ 2 = σ 1 / t + σ 3 (T∆ρ) / t . The standard errorσ 1 of T ∆ρ was com- lution complete to degree/order 180. The ice density contrast 1,753 kg/ puted using the following expression: m3 corresponds to glacial ice density 2,670 kg/m3 (Cutnell and Kenneth, 1995). CRUST2.0 sediment thickness and density data (on 2×2 arc-deg , (15) grid) were used for computing the sediment (density contrast) stripping gravity correction with a spectral resolution complete to degree/order 90.

CRUST2.0 (Bassin et al., 2000) was compiled and administered by the US where γ 0 is normal gravity, , and error Geological Survey and the Institute for Geophysics and Planetary Physics degree potential coefficients. Since CRUST2.0 Moho depths were not at the University of California. CRUST2.0 is an upgrade of CRUST5.1 provided with a standard error model, relative uncertainties (i.e. standard

(Mooney et al., 1998). errors σ 3) of CRUST2.0 Moho depths of 20% were assumed in forming The Earth’s solid topography (i.e. topographical heights onshore and the matrix Q. bathymetric depths offshore) generated on a 2×2 arc-deg grid using the Estimated Moho density contrast taken relative to 2,670 kg/m3 DTM2006.0 coefficients complete to degree/order of 180 is shown in -Fi crust density are shown in Figure 3. The density contrast, was found to gure 1. Maximum topographical heights over the study area reach 4.1 km be between 160 and 682 kg/m3 (mean = 477 kg/m3, standard deviation and maximum bathymetric depths are 5.7 km. = 128 kg/m3). Regional map of refined Bouguer gravity anomalies is shown in Figure Estimated Moho density contrast was compared with 2, values were between -457 and 419 mGal (mean = -43 mGal; standard CRUST2.0. CRUST2.0 Moho density contrast was computed from deviation = 286 mGal). Gravity maxima were found over areas of deepest CRUST2.0 upper mantle densities relative to 2,670 kg/m3 crust den- oceans, and toand gravity minima were located throughout the central part sity. CRUST2.0 Moho density contrast is shown in Figure 4. Diffe- of East Antarctica. rences between both Moho density contrasts are shown in Figures 5. Whereas large variations of Moho density contrast were estima- Results ted using the combined least-squares approach (Fig. 2), the range of CRUST2.0 values was within 580 and 730 kg/m3 (Fig. 4). Such large The combined least-squares method was used for a simultaneous discrepancies (shown in Fig. 5) were likely caused by a low quality estimation of Moho depth and density contrast. The solution was of CRUST2.0 upper mantle density, especially under oceanic crust. obtained by solving the system of normal equations, which was defi- CRUST2.0 upper mantle density under oceanic crust was signifi- ned in equation (11). The observation vector l in equation (10) was cantly overestimated. CRUST2.0 Moho density contrast under the formed by three observation types l1 = T ∆ρ (eqn. 7), l2 = ∆ρ (eqn. Antarctic continental crust had a good agreement with our estimates, 3 8), and l3 = TS. The initial values of Moho depths TS were taken from differences mostly being within ±100 kg/m .

Fig. 4 CRUST2.0 Moho density contrast on a 2×2 arc-deg grid. Fig. 5 Differences between CRUST2.0 and newly estimated Moho density con- Values are in kg/m3. trast on a 2×2 arc-deg grid. Values are in kg/m3. Reference crust-mantle density contrast beneath Antarctica based on the Vening Meinesz-Moritz isostatic inverse problem and CRUST2.0 seismic model

Discussion that started during the Jurassic period when Africa separated from East An- tarctica and proceeded clockwise to its present location in the Ross Emba- Moho density contrast differs significantly in East and West Antarcti- yment and West Antarctica. The almost complete absence of recent seismic ca (see Fig. 3). Moho density contrast maxima are situated throughout the activity suggests that there might not be any undergoing active extension central part of East Antarctica with the extension under the Transantarctic of the rift zone (Cande et al., 2000). Local maxima of the Moho densi- mountain range. Moho density contrast there exceeded 500 kg/m3. Moho ty contrast exceeding ~500 kg/m3 in West Antarctica were found beneath density contrast beneath West Antarctica was less pronounced. A typical Marie Byrd Land. The lithospheric structure there is characterised by topo- range was between 400 and 500 kg/m3, except for local maxima in the graphic doming due to localised hot spot activity (Hole and LeMasurier, central part of Antarctic Peninsula, where values reached ~550 kg/m3. 1994; Winberry and Anandakrishnan, 2004). Ritzwoller et al., (2001) and Block et al., (2009) have estimated that Moho density contrast was typically less than ~350 kg/m3 beneath average crust thickness in the West Antarctica was ~27 km. Average crust oceanic crust; minima were found along the Pacific Antarctic mid-oceanic thickness of ~40 km was estimated for East Antarctica, with maximum ridge. Moho density contrast there was estimated to be as low as 160 kg/ crust thickness being ~45 km. These large differences could be explained m3, corresponding to 2,830 kg/m3 density for the youngest oceanic lithos- by different tectonic and geological compositions of West and East Antarc- phere (Müller et al., 2008). Similar density values have also been found tica. Dalziel and Elliot (1982) proposed that East Antarctica is a single tec- between Antarctic and South-American continental tectonic plates, which tonic block formed predominantly by Craton. Several smaller crust frag- were separated by a newly-formed oceanic lithosphere. ments forming West Antarctica have been moved and further reconfigured with respect to East Antarctica and each other. Ritzwoller et al., (2001) Conclusions and Morelli and Danesi (2004) have analysed shear wave velocities over the whole of Antarctica. They found significant differences in mantle structure Spatial variations of Moho density contrast resembled major features characterised by a low velocity in the West Antarctica while a high velocity of the Antarctic tectonic plate configuration and its geological composi- was detected in the mantle of East Antarctica, with a transition occurring tion. Density contrast maxima were found throughout the central part below the Transantarctic Mountains. Unlike most of similar mountain of East Antarctica with the extension under the Transantarctic mountain ranges, this mountain range was formed in the absence of collision tec- range. Moho density contrast there often exceeded ~500 kg/m3, maxima tonic forces (ten Brink et al., 1997). Several theories have been proposed being 682 kg/m3. Density contrast maxima were found under mountai- explaining possible mechanisms for their formation. Models have included nous ranges and areas covered by the largest continental ice sheet. These thermal buoyancy from an underlying positive temperature anomaly in locations are also characterised by the largest thickness of the Antarctic upper mantle (ten Brink et al., 1997), thicker crust giving the origin to an continental crust, Moho depths there reached ~40 km. isostatically buoyant load (Studinger et al., 2004) or possible collapse of a According to our estimation, Moho density contrast beneath West high-standing plateau with subsequent uplift and denudation (Bialas et al., Antarctica was typically 400 to 500 kg/m3, except for local maxima (~550 2007). The latest models based on integrated geophysical analysis assume kg/m3) in the central part of Antarctic Peninsula. Local minima (400-450 that multiple mechanisms have contributed to the uplift of the Transan- kg/m3) beneath the West Antarctic Rift and the Ross Embayment are likely tarctic Mountains (cf. Studinger et al., 2004; Lawrence et al., 2006). attributed to volcanic compositions throughout this divergent tectonic Despite the central part of East Antarctica being characterised by large zone. variation in continental ice- sheet thickness and rough bedrock topography The largest variations of Moho density contrast were found across of basins and mountain ranges including sub-glacial mountains, significant the East Antarctic continental margin. Moho density contrast beneath the variations in Moho density contrast were almost absent (see Fig. 3). Pre- oceanic crust was typically less than ~350 kg/m3. The extreme minima vailing homogenous Moho density contrast there could be explained by a were detected along the Pacific Antarctic mid-oceanic ridge. more uniform geological structure than that of West Antarctica. The location of the largest local density contrast anomalies correspond to the Gam- References burtsev subglacial mountains, Aurora Basin and Dronning Maud Land. 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